You know the thing with names is that
sometimes they're like real useful at describing things.
Star Wars is war in space.
Star Trek is treks in space.
:O
Both George and Gene grew up with westerns so similarities are unsurprising, but Star Wars was just Lucas writing his own Flash Gordon because he couldn't get rights for the official one. Neither SW nor FG are westerns. Star Trek was picked up when its similarities to a couple of then-popular westerns were highlighted in the pitch. Does that make ST a space western, or does it simply show that someone wanting to write an epic voyage exploring human nature and morality needs to draw comparison to existing popular examples to get it accepted, and at the time those examples happened to be westerns.